Implement tanh

Closes rust-lang/libm#37

library/compiler-builtins/libm/src/lib.rs

@@ -410,7 +410,6 @@ pub trait F64Ext: private::Sealed {
     #[cfg(todo)]
     fn cosh(self) -> Self;
 
-    #[cfg(todo)]
     fn tanh(self) -> Self;
 
     #[cfg(todo)]
@@ -595,7 +594,6 @@ impl F64Ext for f64 {
         cosh(self)
     }
 
-    #[cfg(todo)]
     #[inline]
     fn tanh(self) -> Self {
         tanh(self)

library/compiler-builtins/libm/src/math/mod.rs

@@ -58,6 +58,7 @@ mod sqrt;
 mod sqrtf;
 mod tan;
 mod tanf;
+mod tanh;
 mod tanhf;
 mod trunc;
 mod truncf;
@@ -114,6 +115,7 @@ pub use self::sqrt::sqrt;
 pub use self::sqrtf::sqrtf;
 pub use self::tan::tan;
 pub use self::tanf::tanf;
+pub use self::tanh::tanh;
 pub use self::tanhf::tanhf;
 pub use self::trunc::trunc;
 pub use self::truncf::truncf;

library/compiler-builtins/libm/src/math/tanh.rs

@@ -0,0 +1,52 @@
+use super::expm1;
+
+/* tanh(x) = (exp(x) - exp(-x))/(exp(x) + exp(-x))
+ *         = (exp(2*x) - 1)/(exp(2*x) - 1 + 2)
+ *         = (1 - exp(-2*x))/(exp(-2*x) - 1 + 2)
+ */
+pub fn tanh(mut x: f64) -> f64 {
+    let mut uf: f64 = x;
+    let mut ui: u64 = f64::to_bits(uf);
+
+    let w: u32;
+    let sign: bool;
+    let mut t: f64;
+
+    /* x = |x| */
+    sign = ui >> 63 != 0;
+    ui &= !1 / 2;
+    uf = f64::from_bits(ui);
+    x = uf;
+    w = (ui >> 32) as u32;
+
+    if w > 0x3fe193ea {
+        /* |x| > log(3)/2 ~= 0.5493 or nan */
+        if w > 0x40340000 {
+            /* |x| > 20 or nan */
+            /* note: this branch avoids raising overflow */
+            t = 1.0 - 0.0 / x;
+        } else {
+            t = expm1(2.0 * x);
+            t = 1.0 - 2.0 / (t + 2.0);
+        }
+    } else if w > 0x3fd058ae {
+        /* |x| > log(5/3)/2 ~= 0.2554 */
+        t = expm1(2.0 * x);
+        t = t / (t + 2.0);
+    } else if w >= 0x00100000 {
+        /* |x| >= 0x1p-1022, up to 2ulp error in [0.1,0.2554] */
+        t = expm1(-2.0 * x);
+        t = -t / (t + 2.0);
+    } else {
+        /* |x| is subnormal */
+        /* note: the branch above would not raise underflow in [0x1p-1023,0x1p-1022) */
+        force_eval!(x as f32);
+        t = x;
+    }
+
+    if sign {
+        -t
+    } else {
+        t
+    }
+}

library/compiler-builtins/libm/test-generator/src/main.rs

@@ -717,7 +717,7 @@ f64_f64! {
     sinh,
     sqrt,
     tan,
-    // tanh,
+    tanh,
     trunc,
     fabs,
 }